1. Field of the Invention
The present invention relates to an optical system with compensated spatial dispersion, with an optical axis, with a first optical element, which has a first orientation in relation to the optical axis, and with a second optical element, which has a second orientation in relation to the optical axis, wherein the second orientation is rotated with respect to the first orientation about an angle around the optical axis.
2. Description of the Related Art
Materials for optical systems, such as objectives, lenses, prisms and apparatus including these components and/or elements should be essentially optically isotropic, which means that a light ray or beam passing through them should propagate at the same speed through them in all directions and independently of its polarization. Double refraction or birefringence is a typical sign of different propagation speeds in many crystals. Birefringence usually does not occur in the conventional sense in cubic crystals. However they are optically anisotropic for shorter wavelength radiation. This effect is designated as spatial dispersion and is an intrinsic property of these crystals. A so-called retardation, i.e. a divergence of the wave front, which leads to undesirable interference, occurs because of spatial dispersion, when materials with a cubic crystal structure are used in optical systems. For example, objectives for microlithography are diffraction limited, whereby undesired interference effects lead to poor image production. Shorter wavelength radiation, for example having a wavelength of xcex=157 nm, is used in microlithography. The materials of optical systems that handle this type of short wavelength UV radiation have high or stringent specifications. This short wave radiation can destroy unsuitable materials. For this reason CaF2 is preferred as the material for optical systems used in microlithograph, so that sufficient transmission can be obtained for energetic radiation at these comparatively shorter wavelengths. According to J. H. Burnett, Z. H. Levine, E. Shirley: xe2x80x9cIntrinsic Birefringence in Calcium Fluoride and Barium Fluoridexe2x80x9d, Phys. Rev. B64, 241102(R), 2001, the retardation called for by the spatial dispersion for a wavelength of xcex=157 nm for [110] radiation in a CaF2 crystal amounts to about 11.5 nm/cm. Objectives for microlithography require a retardation of  less than 1 nm/cm because they are diffraction limited. For this reason an optical system is desired, whose spatial dispersion can be limited to a retardation  less than 1 nm/cm, so that for example CaF2 can be used as the material for the optical system for 157-nm radiation in microlithography.
The path differences of the individual rays caused by spatial dispersion differ for different radiation propagation directions in the crystal. It is possible to compensate spatial dispersion, for example, when the propagation direction of a ray in a first optical element is along a so-called rapid axis, which means an axis along which the propagation speed is higher, and in a second optical element along a so-called slow axis, which means an axis along which the propagation speed is reduced. The retardation caused by spatial dispersion is thus compensated in this way, however the compensation is still comparatively insufficient. The residual retardation due to the spatial dispersion always still leads to undesirably large imperfections in the imaging properties of the optical system.
It is an object of the present invention to provide an optical system with elements made from materials with cubic crystal structure, whose spatial dispersion is efficiently compensated, so that only a reduced optical retardation results due to the spatial dispersion.
This object, and others which will be made more apparent hereinafter, are attained by in an optical system having a first optical element and a second optical element arranged along an optic axis, wherein the first optical element has a first orientation in relation to the optic axis and the second optical element has a second orientation in relation to the optic axis.
According to the invention at least one of the first optical element and second optical element is pre-stressed with a compressive stress in a radial symmetric manner with respect to the optic axis in order to compensate for the spatial dispersion. This compressive stress is produced by forces, which are perpendicular to the optic axis and distributed uniformly around the circumference or the optical element.
A stress birefringence may be produced by this compressive stress, which is superimposed on the spatial dispersion. In this way the positions of the fast axis and the slow axis as well as the difference of the propagation speeds occurring on these axes change. Thus the retardation produced by one optical element may be adjusted in this way so that it nearly completely cancels the retardation produced by the other optical element. The size of the required compressive stress may be determined either by experiment, or can be calculated. For this purpose, for example, a so-called ray tracing is performed. Also a commercial ray tracing program, namely Code V of Optical Research Associates, 3280 East Foothill Blvd., Pasadena, Calif., 91197, U.S.A, so that fewer optical stress corrections are necessary.
In a preferred embodiment of the invention the compressive stress is substantially uniform and isotropic. Furthermore the forces exerted by the compressive stress on the optical element are uniform, for example inwardly directed radial symmetric on the outer periphery of a lens. The compressive stress should amount to from 0.5 to 50 MPa, preferably 0.6 to 1.6 MPa.
The first optical element and/or the second optical element should be pre-stressed in a uniform plane stressed state in a plane perpendicular to the optic axis and of course in a radial plane perpendicular to the optic axis in order to provide simpler control and improved computability of the system. This planar stressed state may be produced reproducibly by application of a uniform inwardly directed compressive stress on the periphery.
A stress-producing apparatus is usually used to produce the compressive stress. This stress-producing apparatus usually comprises a collection of devices, which uniformly exert the compressive force on the optical element, especially in a radial direction toward the optic axis. Usual apparatus includes e.g. a clamping ring, a hydrostatic ring, which surrounds the element, such as a tube, or other conventional means, used for producing e.g. an isostatic pressure.
A clamping ring is a device, which produces the radial compressive stress, especially easily. For example, the outer peripheral surface of a lens can be pressed inwardly by means of this clamping ring, so that the clamping or compressive forces act in a radial direction toward the optic axis. It is advantageous when adjusting means for adjusting the compressive force are present. By means of these adjusting means the desired value can be set. Especially during experimental determination of the required compressive stress the compressive stress should adjust the remaining retardation to a minimum value.
In other embodiments of the invention the first optical element is pre-stressed with a first compressive stress and the second optical element is pre-stressed with a second compressive stress different from the first. Thus the retardation of both optical elements can be compensated especially effectively with respect to each other by this pre-stressing with different compressive stresses.
Preferably the material has a cubic crystal structure, such as CaF2 or BaF2. These crystals have especially desirable properties, particular for short wavelength radiation. MgF2 also provides good transmission for short wave radiation.
In the arrangement according to the invention the first and second optical elements have a first and second orientation with first and second axes, which can be both the same and also different, and which can extend parallel to each other or also at an angle to each other. Thus it is of additional advantage, when a so-called fast axis of the first orientation is correlated to or switched with a so-called slow axis of the second orientation. In this case the fast propagation of the wave front in the first optical element along the fast axis can be compensated and/or switched by a slow propagation in the second optical element along the associated slow axis.
In a preferred embodiment according to the invention the optical elements are rotated against each other about the optic axis according to their rotational symmetry in relation to the optic axis. The rotation angle preferably is half the symmetry rotation angle of the material, from which the optical elements are made, or an odd multiple of it, at the respective orientations. In a material with a three-fold symmetry amounting to a symmetry angle 120xc2x0, i.e. the elements should be twisted relative to each other by about half of this angle, thus 60xc2x0 or a 3-fold, 5-fold, 7-fold multiple of it. In a material with an n-fold rotational symmetry with respect to the optic axis, the symmetry angle is 360xc2x0/n. As a result the elements should be rotatably offset against each other by about 0.5*{360xc2x0/n} or an odd multiple of this value.
An advantageous embodiment of the optical system of the invention results when the angle about the optical axis in the first orientation amounts to 45xc2x0, 135xc2x0, 225xc2x0 or 315xc2x0 when the material has a four fold symmetry. This, for example, is the case in a CaF2 crystal when the [100]-, [010]-, [001]-axes are parallel to the optic axis in the first orientation and the second orientation. In this case the (100)-, (010)- and (001)-surfaces of the CaF2 crystal are arranged perpendicular to the optic axis. A rotation about an angle of 90xc2x0 or a multiple of that leads then again to an equivalent arrangement of the crystal and thus the slow axis and the fast axis.
In a crystal with a three-fold rotational symmetry of the material the angle for rotation or twisting about the optic axis should be 60xc2x0, 180xc2x0 or 300xc2x0 in the first orientation. This is then the case when the [111]-, [-1-11]-, [1-11]-axes in the first orientation and the second orientation are parallel to the optical axis. In this case the (111)-, (-1-11)- and (1-11)-surfaces of the crystal are arranged at right angles to the optic axis. A rotation about 120xc2x0, or a multiple of it, leads then to an equivalent origination of the crystal and thus the slow axis and the fast axis.
In a further embodiment of the invention the first optical element and the second optical element have respective surfaces, which are plane/plane or convex/concave or concave/convex and are facing each other. It is however also possible in another embodiment that the facing surfaces are plane/concave or plane/convex. When the facing surfaces are plane relative to each other both optical elements, for example, can be formed as two halves of a convex-convex lens. An inexpensive lens group can be formed by a convex/concave structure or a concave/convex structure. The optical elements can be rigidly connection with other or separated by a gap.
Preferably the first optical element and the second optical element form the end group of an objective. In this embodiment this end group thus compensates for the retardation of the entire system. No other image errors can occur from the end group to the point at which the image forms.
It is also possible that the first optical element and the second optical element form a planar corrective system or component. In this case conventional optics are used, which the first optical element and the second optical element forming the planar corrective system follow. This embodiment is especially preferred when the first optical element and the second optical element are plane layers or disks of equal thickness. A corrective platelet or component thus formed may be simply mounted and simply and easily put in the stressed state.